The explosion of mobile broadband as an essential means of Internet connectivity has made the scalable evaluation and inference of quality of experience (QoE) for applications delivered over LTE networks critical. However, direct QoE measurement can be time and resource intensive. Further, the wireless nature of LTE networks necessitates that QoE be evaluated in multiple locations per base station as factors such as signal availability may have significant spatial variation. Based on our observations that quality of service (QoS) metrics are less time and resource-intensive to collect, we investigate how QoS can be used to infer QoE in LTE networks. Using an extensive, novel dataset representing a variety of network conditions, we design several state-of-the-art predictive models for scalable video QoE inference. We demonstrate that our models can accurately predict rebuffering events and resolution switching more than 80% of the time, despite the dataset exhibiting vastly different QoS and QoE profiles for the location types. We also illustrate that our classifiers have a high degree of generalizability across multiple videos from a vast array of genres. Finally, we highlight the importance of low-cost QoS measurements such as reference signal received power (RSRP) and throughput in QoE inference through an ablation study.